Blurry photos while using my Nikon, 55-200m lens

So I was out taking photos of my brothers baseball game. He was pitching, and I of course was standing behind the fence ( home plate/dugout ). Anyways I have a D3000 and was using my kit lens ( 55-200m) for distance. I had it on S, Iso 200, and it was about 530. Still had nice sunlight. I was zoomed out all the way, and I couldn't get my shutter speed above 125 without it saying, too low light. Basically, I got home and all photos are so grainy. I'm not sure what I was doing wrong. Any suggestions?

That lens is not "fast", meaning it does not have a constant, large aperture such as 2.8. When zoomed out, it is closing Way down on you severely restricting light. To use it, you are going to HAVE to raise the ISO well above 200. Probably more like 800 or 1000, maybe even higher. Ideally, if you plan to do this kind of shooting on a regular basis, you need a MUCH better lens.

Sports like that you want a fast shutter speed. Now.let's talk us about it and save you the hassle of actually reading and learning.

iso 400 would get you 1/250
iso 800 would get you 1/500

That's still not that much but a lot more. I'd set it on 800 and cheat a bit and set the shutter speed on 1/640 and ignore the warnings. Shoot half a dozen and check how bad they are.

Was the lens clean?
image stabilisation on?
you should probably have set it to aperture priority not shutter priority…

then the aperture would set the shutter speed…

You can fix the grain in post processing. Shoot in RAW. Then process the noise out with your RAW conversion software.

You probably need to bump up the ISO more than 200 to get the shutter fast enough for an action shot.

An ISO setting of 200 wouldn't achieve much in low light. If you can't afford a fast lens, don't be afraid to jack up the ISO all the way up to, say 1600 if the shot is important to you and you could live with a bit of grain. Your photograph may have a light grain but still you will get a sharp, non-blurry shot.
In your situation you told the camera to use ISO 200 setting and the camera obligingly told you not enough light when you tried to use a fast shutter speed. If you used, for instance, ISO400 you could have used a shutter speed twice as fast.

In bright light that should have worked fine. The rule of thumb is to have your shutter speed the same number as the lens length, so if you were zoomed out to 200mm, you should shoot at least 1/200 of a second. With the camera on S, it should set your aperture appropriately.

my photos are coming out blurry when I use my 55-200mm lens on my Nikon camera